WASHINGTON (CNN) -- The Senate's top Democrat said Tuesday that he will force a vote on Thursday on whether to open debate on tougher gun laws, increasing pressure on legislators from both parties negotiating a possible compromise on a package that some Republicans have threatened to filibuster.

A GOP filibuster would mean Senate Majority Leader Harry Reid needs 60 votes to begin Senate consideration of the package based on proposals by President Barack Obama in the aftermath of the Newtown school massacre in December that killed 20 first-graders and six educators.

Obama has made the gun measures a major focus of his second-term agenda, holding events across the country to push for Congress to vote on the package. He spoke Monday in Connecticut, the state where the Newtown shootings occurred.